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Question
(x+2x)^2 = 8(y-3)i need the directrix vertex and  focus

Answer
are you sure you typed this correctly, because

(x + 2x)^2 = 8(y - 3)i

becomes

(3x)^2 = 8(y - 3)i

9x^2 = 8i(y - 3)

4p = 8i
p = 2i

Directrix : y = k - p, y = 3 - 2i
focus : (h, k + p), (0,3 + 2i)

Vertex : (0,3)
Focus : (0,(3 + 2i))
Directrix : y = 3 - 2i

info found at www.sinclair.edu/centers/mathlab/pub/findyourcourse/worksheets/116,117/ConicSections.pdf

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